One of the major challenges (Mazziotta and Koslow, 1987) to effective quantitative functional imaging via PET or SPECT is the detailed association of function with anatomy. Recent developments in morphometrics, the geometrical measurement of biological shape variation and shape change, have merged classic ideas from multivariate statistical analysis-notably, ideas of regression and optimal prediction-with an intuitively attractive approach to shape change as deformation. Extending and exploiting these developments, we intend to study the statistical features of certain computations crucial to the regional quantification of functional images: the accuracy of optimally estimated "anatomical maps" superimposed over those images, and the accuracy of functional parameters imputed to specific regions of the basis of those maps. We will proceed by applying three techniques of the new morphometrics: interpolation of discrete point correspondences via thin-plate splines, resolution of correspondence between curving structures according to a criterion of minimum global nonlinearity, and the coordinate- independent analysis of configurations of arbitrarily many labeled points as a single vector of shape variables. We will first select a conventionalized "Atlas" of normative MRI anatomy: a roster of identifiable points and curving structures. After the necessary morphometric techniques have been coded for application to three-dimensional data, we shall determine, for each of two samples totalling 40 normal patients, a thin-plate spline warping function that deforms the Standard MRI Atlas into the traced version of the patient's MRI scan. The dependence of the accuracy of this mapping upon the complexity of the data description will be explored. At the same time, there will be selected a series of landmark points visible upon the paired PET image and presumed to correspond to homologous points visible via MRI. Using the statistical technique of Partial Least Squares, we will generate a regression of the observed MRI warping function (at some particular level of accuracy) upon the configuration of PET landmarks. The regression function which results takes, case by case, a set of landmarks individual case. The accuracy of this predicted warping function will be calibrated using a set of patients not involved in the computation of the regression formula. This "accuracy" has two aspects: a measure of geometrical precision, in root-mean square millimeters, and also a measure of precision of certain derived functional quantities, in root-mean-square mu curies or mu curies/cc of activity. These morphometric functional imaging techniques will be of great use in further calibrations of the anatomy of the PET image in studies of diverse clinical conditions and in the assessment of direct interventions upon normal metabolic function.